Prism

Prism is a three-dimensional solid object in which the two ends are exactly of the same shape. It is the combination of the flat faces, identical bases and same cross-sections. The faces are parallelograms without the bases. If you take the cross-section of the prism parallel to the bases, the cross-sections will look like the bases. In this article, let us have a complete explanation about the types and also how to find the volume and area of a prism.

Prism

Types of Prism

Depends upon the shape of the bases, the prisms are named. It is of two types, namely

  • Regular Prism
  • Irregular Prism

Regular Prism: If the bases of the prism are a regular polygon, it is called regular prism

Irregular Prism: If the bases are an irregular polygon, then the prism is called as an irregular prism.

Right Prism Vs Oblique Prism

Apart from this, the prism can be classified into

  • Right Prism
  • Oblique Prism
Right Prism Oblique Prism
If the faces and the joining edges are perpendicular to the base faces, then it is known as right prism If the faces and the joining edges are not perpendicular to the base faces, then it is known as oblique prism
In right prism, the side faces are rectangles In an oblique prism, the side faces are parallelograms

Based on the shape of the bases, it is further categorised in different types, namely

Prism Type Base Shape
Triangular Prism Triangle
Square Prism Square
Rectangular Prism Rectangle
Pentagonal Prism Pentagon
Hexagonal Prism Hexagon

Surface Area of a Prism

Surface Area of a Prism

For any kind of prism, the surface area can be found using the formula

Surface Area of a Prism = 2(Base Area)+ (Base perimeter × length)

Volume of a Prism

The volume of the prism is defined as the product of the base area and the prism height

Therefore,

The volume of Prism = Base Area × Height

For example, if you want to find the volume of a square prism, you must know the area of a square, then its volume can be calculated as follows:

The volume of a square Prism = Area of square×height

V = s2 × h cubic units

Where “s” is the side of a square.

Prism Problems

Example 1:

Find the volume of a triangular prism whose area is 60cm2 and height is 7cm?

Solution:

Given:

Area = 60 cm2

Height = 7 cm

We know that,

The volume of a prism = Base area × Height cubic units

Therefore, V = 60 ×7 = 420

Hence, the volume of a triangular prism = 420 cm3.

Example 2:

Find the height of the square prism whose volume is 360 cm3 and the base area is 60 cm2?

Solution:

Given:

The volume of a square prism = 360cm3

Base Area = 60cm2

Therefore, the height of the square prism is calculated as follows:

The volume of square prism = Base area × height

360 = 60 × prism height

Therefore, the height,h = 360/60

Prism Height, h = 6 cm.

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